Given $a \star b = a^2 + 2ab + b^2$, what is the value of $a \star b$ when $a = 4$ and $b = 6?$
Note that $a \star b = a^2 + 2ab + b^2 = (a + b)^2$. Thus, $4 \star 6 = (4 + 6)^2 = 10^2 = \boxed{100}$.